Expanding the Computation of Mixture Models by the use of Hermite Polynomials and Ideals

TL;DR

This paper introduces a novel method using Hermite polynomials and ideals to extend mixture models, enabling the combination of different distribution families beyond traditional parametric constraints.

Contribution

It presents a new approach that allows mixture models to incorporate diverse distribution families through Hermite polynomial techniques.

Findings

Enables modeling of mixtures from different distribution families.

Extends the applicability of mixture models beyond Gaussian or Poisson.

Provides a mathematical framework for combining diverse distributions.

Abstract

Mixture models have found uses in many areas. To list a few: unsupervised learning, empirical Bayes, latent class and trait models. The current applications of mixture models to empirical data is limited to computing a mixture model from the same parametric family, e.g. Gaussians or Poissons. In this paper it is shown that by using Hermite polynomials and ideals, the modeling of a mixture process can be extended to include different families in terms of their cumulative distribution functions (cdfs)